Ultra-precision machining by the cylindrical polishing process

A process planning method for removing an arbitrary and axially symmetric error profile by the cylindrical polishing process (abbreviated as the CPP process) is proposed in this study. This method is to plan the dwelling-time of the polishing tool so that the error profile can be accurately removed. The tool dwelling-time distribution is solved by a non-negative least square method. By using this method, the residual error between actual and desired removal depths may be induced. It is shown that the residual error is related to the width of the machining zone, the wavelength of the error profile, and the tool’s resolution. The computer simulations indicate that the residual error is always negligible when the wavelength of the error profile is larger than the width of the machining zone. If the wavelength of the error profile is large, a small size of the tool’s resolution is found effectively to reduce the residual error. The experimental study confirms that an arbitrary error profile can be accurately removed on the basis of the proposed method.     

A process planning strategy for removing arbitrary and axially symmetric profile by a polishing process

In this study, a machining strategy for a polishing process to remove an arbitrary and axially symmetric profile is proposed. The strategy is to plan the tool motion so that a desired profile can be accurately machined. From the volume removing analysis of a polishing process, it is suggested that the dwelling time of the tool at a position should be a linear function of the product of the depth to be removed by its corresponding radius. By using this strategy, three types of errors may be induced: the machining time–distribution error, the ripple error and the resolution error. It is shown that these errors are related to the profile, the tool step, the volume removing rate and the size of the machining zone. The qualitative and quantitative properties of these errors are analyzed. This analysis indicates that a dominant factor in deciding these errors is the tool step size. By increasing this size, both the machining time–distribution error and the resolution error are reduced but the ripple error is enhanced. A tactic is proposed to solve the conflict in choosing the tool step. The experimental study conforms that the proposed strategy can accurately remove an arbitrary profile and the error analysis is reasonable.     

A process planning strategy for removing an arbitrary profile by hydrodynamic polishing process

A process planning strategy for removing an arbitrary profile by a deterministic polishing process is proposed. This strategy suggested that to remove an arbitrary profile the time-distribution of the tool motion at themachining area can be designed to be a linear function of the profile. Because the area of the instantaneous machining zone is finite and the machining rate distribution at this zone is not uniform, this strategy may cause a difference between the desired and machined profiles. The possible errors are classified into two groups: the machining time-distribution error and the ripple error. It is shown that the machining time-distribution error is significant only at the boundary of the machining area. By increasing the size between two conjoint tool positions, this error can be reduced. The size of the instantaneous machining zone has little effect on this error if the size ratio between this zone and two conjoint tool positions is fixed. On the other hand, the ripple error will occur over the whole machining area. The smaller the distance between two conjoint tool positions, the smaller the ripple error will be. The experimental study indicated that the analytical prediction is correct and an arbitrary profile can be accurately removed according to this proposed strategy.     

Optimized feed scheduling in three axes machining. Part I: Fundamentals of the optimized feed scheduling strategy

An optimized feed scheduling strategy is proposed in this paper to maximize the metal removal rate in 3-axis machining while guaranteeing the machining accuracy. The tool path is assumed defined by a cubic parametric form. In part I of this paper, the fundamentals of this strategy are presented. This strategy integrates the feed drive dynamics, described by the acceleration/deceleration (Acc/Dec) profile, with the minimum-time trajectory planning in order to achieve the desired feed rate at the appropriate position. An optimum use of the feed drive capabilities is considered to track the changes in the cutting geometry along the tool path and to ensure an acceptable contour error. Therefore, this strategy combines different constraints and various criteria in modifying the feed rate to maintain a near-constant cutting force resulting in a highly non-linear problem. The constraints include the cutting force magnitude, the feed rate boundaries, the contour error and the characteristics of the (Acc/Dec) profile of the different feed drive systems. The criteria are the maximum production rate, the machining accuracy and safety. In part II of this paper, the effectiveness of this strategy is demonstrated using ball end mill operation on a workpiece that provides variable cutting geometry along a non-linear tool path. The performance of this strategy in terms of productivity, machining safety, and machining accuracy, is compared to a feed scheduling strategy based on control points as well as to milling with constant feed rate.     

Reduction of tool wear during hydrodynamic polishing: A ‘rock-and-roll’ polishing strategy

In this paper, a ‘rock-and-roll’ polishing strategy is proposed for reducing the influence of tool wear on machining rates during hydrodynamic polishing. An analytical study suggests that the radius of curvature of spherical tools changes rapidly during the tool wear process. In addition, variations in the tool radius have a significant effect on machining rates. Increasing the contact length of the tool rapidly decreases the variation in the tool's radius of curvature. A rock-and-roll polishing strategy is therefore proposed to increase the contact length of the tool. This strategy is proposed to design the tool's rocking motion with an appropriate dwelling-time distribution so as to increase the area (or contact length) of the wear zone and create a uniform wear depth, which will in turn reduce the variation in the tool radius. A separate volume removing analysis of the tool wear suggests that the dwelling time of a tool at a given position can be determined for a given wear depth and wear rate. Finally, an experimental study confirms that the proposed strategy can reduce the variation in the tool's radius of curvature and that the effect of tool wear on the machining rate can be suppressed.     

偏置量对固结磨料小工具头抛光面形收敛效率的影响

目的 解决自由曲面磨抛面形收敛困难的问题,提高抛光小工具头的抛光效率.方法 提出一种偏置式固结磨料小工具头,基于固结磨料小工具头的结构特征参数,建立抛光小工具头的去除函数理论模型,并进行仿真分析,应用定点抛光法建立抛光小工具头去除函数实验模型,并验证抛光小工具头理论去除函数合理性,基于CCOS技术原理建立工件表面定量去除模型,通过虚拟加工实验探索偏置量对固结磨料小工具头抛光钛合金后的面形收敛效率的影响.结果 归一化理论去除函数曲线与实验曲线吻合度较高,定点抛光去除函数仿真模型能够很好地预测定点抛光斑的去除轮廓形状.抛光小工具头抛光钛合金的面形误差随偏置量增加,呈现先减小、后增大的趋势,无偏置的抛光小工具头抛光后,面形数据均方根(RMS)收敛效率为54.56％,波峰值与谷峰值之差(PV)的收敛效率为60.21％,当抛光小工具头偏置量为1.5 mm时,抛光后的RMS收敛效率达到最高,为73.83％,PV收敛效率为69.68％.结论 固结磨料小工具头去除函数理论模型可指导确定性材料去除,偏置量为1.5 mm时的抛光小工具头具有最强的修正误差能力,可以显著提高固结磨料小工具头抛光工艺的面形收敛效率.     

Fabrication of free-form surfaces using a long-stroke fast tool servo and corrective figuring with on-machine measurement

Fabrication of free-form surfaces that are frequently demanded for the construction of optical imaging systems is described. To obtain a tool motion with large amplitude and high bandwidth, a novel long-stroke fast tool servo is proposed and installed on the Z-axis of a diamond turning machine as an additional synchronized axis. In addition, a special on-machine measurement device is used to measure the optical parameters of the machined surface and to compensate for the residual form of errors that are commonly produced in the diamond turning process. Actual machining test results show that the proposed procedures are capable of generating the copper free-form mirrors of 50 mm diameter to a form accuracy of 0.15 μm in peak-to-valley value error.     

Surface and geometry error modeling in brittle mode grinding of ophthalmic lenses moulds

The selection of modeling and machining parameters for glass mould fabrication in ophthalmic lenses production, has required the definition of a theoretical–empirical model of the ground surface in order to predict the overall geometry errors of the surface. The accurate control of the geometrical errors and of the surface texture for the mould functional surface is crucial for the subsequent polishing operation, which is responsible for the final geometry, surface finish and cost. The basic hypotheses validation has been accomplished by measuring the micro-geometric parameters P, W and R and by characterizing the macro-geometry comparing the nominal profile and the measured profile. The correspondence among theoretical hypotheses and experimental results allows realistic predictions of the attainable surface texture during a contour grinding operation and the adoption of preventive actions in order to compensate the geometrical errors due to modeling and tool path generation parameters.     

Ultra-precision machining by the hydrodynamic polishing process

This study will examine the feasibility of applying the hydrodynamic polishing (HDP) process as an ultra-precision machining method, which is aimed to compensate the form error of a work surface so that the form precision is improved. To be an ultra-precision machining method, the HDP process is required to have a deterministic machining nature and to have the capability to machine an arbitrary shape. From the machining mechanism, four sets of parameters that dominate the deterministic properties of the process are identified. It is clearly demonstrated from the experimental study that the HDP process is deterministic if the identified parameters are well controlled. To machine an arbitrary shape, a machining principle is proposed. From this principle, a square slot with uniform depth and a semi-cylindrical profile with parabolic cross-section can be accurately obtained by the HDP process. Hence, the HDP process can be a promising method to compensate form error for the ultra-precision purpose.     

数控机床动态轨迹误差仿真与优化研究

在介绍数控机床加工轨迹运动控制原理的基础上,对数控机床动态轨迹误差进行了仿真研究,得出数控机床动态轨迹误差与拟加工曲线的曲率和机床进给速度相关的结论。在待加工的工件几何曲线曲率已定情况下,提出了变进给速度的数控机床动态轨迹误差优化策略,仿真结果表明:该控制策略能够有效地减少机床动态轨迹误差量,提高相关轨迹曲线的加工精度。     

A new apparatus for finishing large size/large batch silicon nitride (Si3N4) balls for hybrid bearing applications by magnetic float polishing (MFP)

A new apparatus was designed and built for the finishing of large size/large batch silicon nitride (Si₃N₄) balls by magnetic float polishing (MFP) technology for hybrid bearing applications. The polishing chamber is so designed that during polishing it can self-align with the upper part of the polishing chamber connected to the spindle. In situ machining of the upper part of the chamber is performed on the machine tool in which the apparatus is located, in order to achieve high accuracy and geometric alignment of the system. The finishing methodology consists of mechanical polishing followed by chemo-mechanical polishing. Boron carbide (B₄C), silicon carbide (SiC), and cerium oxide (CeO₂) are the three abrasives used in this investigation. Three stages are involved in polishing, namely, 1. a roughing stage to remove maximum material without imparting any damage to the surface, 2. an intermediate stage of semi-finishing to control the size and improve sphericity, and 3. a final finishing stage to obtain best surface finish and sphericity while maintaining the final diameter. Taguchi method was applied for the roughing stage to optimize the polishing conditions for the best material removal rate. Level average response analysis has indicated that a load of 1.5 N/ball, an abrasive concentration of 20%, and a speed of 400 rpm would give a high material removal rate using B₄C (500 grit) abrasive. A groove is formed on the bevel of the upper part of the chamber which plays different roles, some beneficial and other not so beneficial, in each stage. In the roughing stage, it is preferable, though not essential, to machine the groove after each run to maintain high material removal rates. It is, however, necessary to remove the groove formed at the end of the roughing stage. In the intermediate or semifinishing stage, sphericity can be significantly improved by not machining the groove. Thus groove, in this case, facilitates in the improvement of sphericity. Before the beginning of the final finishing stage, machining the groove is necessary for rapid improvement in the surface finish. A batch of 46, 3/4 in. Si₃N₄ balls was finished to a final diameter of 0.7500 in. with an average sphericity of 0.25 μm (best value of 0.15 μm) and an average surface finish, Ra of 8 nm (best value of 6.7 nm) with an actual polishing time of <30 h. This technology is easy to implement in industry and does not entile high capital investment.     

High-precision machining by measurement and compensation of motion error

This paper describes a systematic method to model and compensate geometric errors of machine tools. In order to separate geometric errors from other errors, measured errors are analyzed in the frequency domain by using the Fourier series. Then, the frequency components corresponding to geometric errors are selected based on the repeatability of their wavelength. Finally, the components are reconstructed and forwarded for the compensation by a fine motion drive. A CNC machine tool with a fine motion mechanism on the Z-axis was developed to compensate the error components in the Z direction on the XY plane. A flat surface machining with non-rotational cutting tools was tested to validate our approach. On the plane of 45 mm×70 mm, the fluctuation of the relative displacement was reduced from 1.3 to 0.5 μm P-V. Machining experiments with a single-crystal diamond tool were also carried out and the straightness of the profile curve was reduced from 1.0 to 0.4 μm. The result of the experiments showed that the geometric errors were compensated separately from the vibration due to the bending mode of the machine column.     

Mechanism of mid-spatial-frequency waviness removal by viscoelastic polishing tool

Nanoscale roughness with ultra-precise form control can be readily achieved using compliant finishing methods such as bonnet polishing. However, their weak point lies in the difficulty of removing mid-spatial-frequency (MSF) waviness in the typical range from 0.1 to 5.0 mm wavelength. To overcome this shortcoming, a bonnet tool filled with viscoelastic fluid is developed and a comprehensive model is established to disclose its distinct removal behavior in the MSF range. The model considers tool viscoelasticity, stress distribution and workpiece topography. Experiments show high consistency with theoretical predictions, and show that MSF waviness can be effectively reduced using the proposed method.     

基于力控传感器的自动打磨误差补偿方法

针对钛合金机匣某部位打磨过程中装夹与加工轨迹存在误差导致欠打磨或过打磨的问题,文章提出了一种基于该系统的在线误差补偿方法。该方法首先通过力控传感器测量加工位置轮廓,然后计算误差大小并控制旋转工作台转动,调整工件的角度,最后对加工轨迹进行修改,以实现打磨过程中对误差的补偿。通过实验发现补偿后的打磨表面质量明显提高,因此该方法对提高钛合金机匣的自动化打磨质量有重要的指导和参考意义。     

Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors

The paper presents the design of a six-axis machining system and its application in fabricating large off-axis aspherical mirrors with sub-aperture lapping techniques. The new system is based on computer-controlled optical surfacing (CCOS), which combines the faculties of grinding, polishing, and on-machine profile measuring, has the features of conventional loose abrasive machining with the characteristics of a tool having multiple degrees of freedom moving in planar model. And a novel dual touch-trigger probe profiler is designed, which is composed of a probe, model METRO-MT60 made by HEIDENHAIN Co., is integrated into the system for measuring the shape accuracy of the tested aspherical surface, another probe modeled METRO-MT12 is designed as a calibrating device for minimizing the cosine error caused by assembly inaccuracy. The new CNC machining system with two kinds of moving coordinate systems, dual tool activities and on-machine measuring is presently developed based on the new concept. The general material removal function during machining is analyzed on the basis of the Preston hypothesis. Further, an alignment test of the measuring profiler is carried out using a leveling rule as a specimen. The accuracy of the optical surfaces measured by the dual probe profiler is found to be within 1 μm PV after removing cosine error and error compensating, achieves to the resolving power of the profiler is about 0.2–0.5 μm, so the developed system can be applied to the shape accuracy measuring of aspheric fabrication with micro precision during fine grinding process according to the calibrating results. Finally, the manufacturing experiments are carried out by virtue of an off-axis oblate ellipsoid mirror with rectangular aperture as 770 mm×210 mm and centered 127 mm. The accuracy of the aspherical mirror improved from the initial form error of 17.648 μm rms to the final one of 0.728 μm rms after grinding for 200 h.     

磁流变抛光非球柱面镜的新工艺

高精密的柱面镜光学元件,不但要求其具有极低的表面粗糙度、无表面/亚表面损伤和低的残余应力等,而且需要保证其柱面母线的平行度与垂直度。通过分析传统磨研抛技术和计算机控制的光学表面成型技术(CCOS) 2种技术对柱面镜加工后的表面粗糙度、面形精度和母线误差的影响,归纳2种加工方法的优缺点,针对现有加工方法存在的低效率、高粗糙度、表面/亚表面损伤等问题提出一种具有对称结构的非球柱面镜磁流变抛光新工艺,并通过时间参数实验验证了新工艺的可行性。该工艺降低了柱面镜的表面粗糙度,提高了面型精度,在抛光时间为40 min时,表面粗糙度R_a从1.84 μm降低至0.36 μm,局部面型精度RMS₁从 1.91 μm降低到0.24 μm,母线截面面型精度RMS₂从4.1 μm下降到0.68 μm。      

The analysis of correlative error in principal axis method for five-axis machining of sculptured surfaces

Correlative error is a kind of error between the cutter locations. This text presents a detailed analysis about correlative error in the principal axis method (PAM) that is a strategy of tool positioning for five-axis machining. It points out all the strategies based on linear projection cannot avoid this interference and cannot be disregarded especially in the strategies with large stepover. Accurate calculating is made individually on linear and curve feed and formulae are developed. The author also gave the available application range of PAM and the algorithm for estimating correlative error.     

动态磁场集群磁流变抛光加工机理及试验研究

基于动态磁场集群磁流变平面抛光的加工机理以及动态磁场作用机理,对单晶硅基片进行动态磁场集群磁流变抛光试验研究。结果表明:动态磁场能使畸变的抛光垫实时自修复,磨料具有频繁的动态行为,克服了静态磁场作用下抛光垫变形难恢复且磨料堆聚的缺点,使材料去除过程稳定,抛光效果较好;在动态磁场作用下,不同抛光方式的加工效果也不同;在多工件同步抛光中,大尺寸的工具头高速自转使工件表面有更高的线速度,磨料对单晶硅表面缺陷去除作用更强。经过5 h抛光,硅片表面粗糙度R_a由0.48 μm下降到3.3 nm,获得超光滑表面。      

基于响应面法的钛合金Halbach阵列增强磁流变抛光工艺参数优化

目的 提高钛合金磁流变抛光的表面质量和抛光效率。方法 用Halbach磁场阵列强化磁场,通过载液盘与磁铁反向旋转来增强磁流变抛光效率,使抛光头拥有更强的恢复性与自锐性。通过仿真模拟和实际测量对比研究Halbach阵列与N-S阵列的磁场分布和磁场梯度。依照试验结果描述抛光剪切力、表面粗糙度与表面微观形貌随时间的变化规律。采用响应面法优化载液盘转速、磁铁转速和加工间距等3个工艺参数,建立剪切力和表面粗糙度的拟合方程数学预测模型,并对其中的不显著项进行优化。结果 在响应面交互作用分析中,工艺参数对剪切力的影响的大小顺序为加工间距、磁铁转速、载液盘转速;对表面粗糙度影响的大小顺序为载液盘转速、磁铁转速、加工间距。根据不同的需求,确定选定范围内的工艺参数组合,需要快速去除材料时,使剪切力趋于最大值的工艺参数组合为载液盘转速227 r/min,磁铁转速64 r/min,加工间距0.1 mm,通过20 min抛光后得到了表面粗糙度Sa为34.911 nm的光滑表面。抛光过程中,钛合金抛光所受剪切力τ为0.812 N。需要最优表面质量时,使表面粗糙度值趋于最小值的工艺参数组合为载液盘转速300 r/min,磁铁转速150 r/min,加工间距0.1 mm,通过20 min抛光后得到了表面粗糙度Sa为26.723 nm的光滑表面。抛光过程中,钛合金抛光所受剪切力τ为0.796 N。结论 Halbach阵列拥有较高的磁场强度和富有空间变化的磁感线,能够使磁流变液中的磁链呈现出更多的姿态变化。根据响应面法优化后的剪切力和表面粗糙度预测模型,预测结果与验证试验结果相差很小,预测模型的准确度与可信度较高。